Gravity Gradiometer Instruments (GGI) are used to detect very small spatial variations (gradients) in the acceleration due to gravity. Gravity gradients are affected by non-uniform mass distributions. In one non-limiting example, GGIs are used in mineral and hydrocarbon exploration, where GGIs are used to survey above areas of the Earth's surface. Density variations in the subsurface rock formations, indicative of oil or gas deposits, create gravity gradients that are measurable by the GGIs, enabling the identification of subsurface prospects.
GGIs utilize one or more accelerometers which operate in combination to detect gravity gradients. Typically, e.g., in conventional configurations, the accelerometers are carefully arranged on a disk substrate about a rotational axis defined substantially at the center of the disk. The disk provides a known distance between accelerometers which can be used to calculate differences in acceleration experienced by different accelerometers. The differential accelerations are divided by the characteristic dimension or baseline to produce measured gravity gradients or a spatial difference over the known distance.
Gravity gradients are miniscule in comparison to other forces and accelerations to which the accelerometers are exposed. For example, in an application where the GGI is installed in an aircraft to perform an airborne survey, the motion of the aircraft exposes the accelerometers to kinematic accelerations which are many orders of magnitude larger than the differential accelerations associated with the gravity gradients that the GGI is intended to measure. Dynamic loading from the motion of the aircraft, its onboard vibration environment, or local dynamic deformations at an accelerometer mount location, as well as aspects of accelerometer resulting from its fabrication create additional complexities and accelerometer responses/outputs which must be addressed in order to identify the gravity gradients. If the raw output of the accelerometer was taken and digitized to produce an overall signal, the portion of the signal representing the differential acceleration owing to gravity gradients would be effectively lost due to the excessive disturbances of much greater magnitude than the gravity gradient-based accelerations. Therefore, these environmental disturbances must be identified and removed to leave the sought gravity gradient influence. In some applications, an electromagnet is placed within the path of a pendulum on which a proof mass is attached and swings in response to accelerations experienced by the accelerometer. A rebalancing current is generated based on an error voltage that is representative of the environmental error sources, and is applied to the electromagnet to constrain the pendulum mass in its proper position while under the influence of external forces.
The identification and removal of external forces presents challenges which when addressed, affect the sensitivity and bandwidth of the GGI. Gravity gradients are typically very low magnitude signals, while the error sources produce signals with much greater magnitudes. Furthermore, in a GGI having multiple accelerometers, each accelerometer is rebalanced individually, which further decreases the overall sensitivity of the GGI. In conventional GGIs, accelerometers are paired off and paired accelerometers are arranged on the disk opposite one another. These opposing output signals are added together in an attempt to cancel error signals which do not relate to gravity gradients. The configuration requires careful considerations regarding placement of the pairs of accelerometers. The disk is rotated, which modulates the sought differential accelerations associated with gravity gradients to a center frequency of twice the spin rate and simultaneously providing spectral separation from the common plumb gravity influence. Mechanization of the rotating structure introduces other sources of noise due to the rotational mechanism of the rotating disk. Improved mechanisms which rebalance a GGI having an arbitrary number of accelerometers are desired.